<html><head><title>R: European Option evaluation using Closed-Form solution</title>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<link rel="stylesheet" type="text/css" href="../../R.css">
</head><body>

<table width="100%" summary="page for EuropeanOption {RQuantLib}"><tr><td>EuropeanOption {RQuantLib}</td><td align="right">R Documentation</td></tr></table>
<h2>European Option evaluation using Closed-Form solution</h2>


<h3>Description</h3>

<p>
The <code>EuropeanOption</code> function evaluations an European-style
option on a common stock using the Black-Scholes-Merton solution. The
option value, the common first derivatives ("Greeks") as well as the
calling parameters are returned.
</p>


<h3>Usage</h3>

<pre>
EuropeanOption.default(type, underlying, strike, dividendYield, riskFreeRate, maturity, volatility)

## S3 method for class 'Option':
plot
## S3 method for class 'Option':
print
## S3 method for class 'Option':
summary
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>type</code></td>
<td>
A string with one of the values <code>call</code> or <code>put</code></td></tr>
<tr valign="top"><td><code>underlying</code></td>
<td>
Current price of the underlying stock</td></tr>
<tr valign="top"><td><code>strike</code></td>
<td>
Strike price of the option</td></tr>
<tr valign="top"><td><code>dividendYield</code></td>
<td>
Continuous dividend yield (as a fraction) of the stock</td></tr>
<tr valign="top"><td><code>riskFreeRate</code></td>
<td>
Risk-free rate</td></tr>
<tr valign="top"><td><code>maturity</code></td>
<td>
Time to maturity (in fractional years)</td></tr>
<tr valign="top"><td><code>volatility</code></td>
<td>
Volatility of the underlying stock</td></tr>
</table>

<h3>Details</h3>

<p>
The well-known closed-form solution derived by Black, Scholes and
Merton is used for valuation. Implied volatilities are calculated
numerically.
</p>
<p>
Please see any decent Finance textbook for background reading, and the
<code>QuantLib</code> documentation for details on the <code>QuantLib</code>
implementation.
</p>


<h3>Value</h3>

<p>
The <code>EuropeanOption</code> function returns an object of class
<code>EuropeanOption</code> (which inherits from class 
<code><a href="Option.html">Option</a></code>). It contains a list with the following
components:
</p>
<table summary="R argblock">
<tr valign="top"><td><code>value</code></td>
<td>
Value of option</td></tr>
<tr valign="top"><td><code>delta</code></td>
<td>
Sensitivity of the option value for a change in the underlying</td></tr>
<tr valign="top"><td><code>gamma</code></td>
<td>
Sensitivity of the option delta for a change in the underlying</td></tr>
<tr valign="top"><td><code>vega</code></td>
<td>
Sensitivity of the option value for a change in the
underlying's volatility</td></tr>
<tr valign="top"><td><code>theta</code></td>
<td>
Sensitivity of the option value for a change in t, the
remaining time to maturity</td></tr>
<tr valign="top"><td><code>rho</code></td>
<td>
Sensitivity of the option value for a change in the
risk-free interest rate</td></tr>
<tr valign="top"><td><code>dividendRho</code></td>
<td>
Sensitivity of the option value for a change in the
dividend yield</td></tr>
<tr valign="top"><td><code>parameters</code></td>
<td>
List with parameters with which object was created</td></tr>
</table>

<h3>Note</h3>

<p>
The interface might change in future release as <code>QuantLib</code>
stabilises its own API.
</p>


<h3>Author(s)</h3>

<p>
Dirk Eddelbuettel <a href="mailto:edd@debian.org">edd@debian.org</a> for the <font face="Courier New,Courier" color="#666666"><b>R</b></font> interface;
the QuantLib Group for <code>QuantLib</code>
</p>


<h3>References</h3>

<p>
<a href="http://quantlib.org">http://quantlib.org</a> for details on <code>QuantLib</code>.
</p>


<h3>See Also</h3>

<p>
<code><a href="EuropeanOptionImpliedVolatility.html">EuropeanOptionImpliedVolatility</a></code>,
<code><a href="EuropeanOptionArrays.html">EuropeanOptionArrays</a></code>,
<code><a href="AmericanOption.html">AmericanOption</a></code>,<code><a href="BinaryOption.html">BinaryOption</a></code>
</p>


<h3>Examples</h3>

<pre>
# simple call with unnamed parameters
EuropeanOption("call", 100, 100, 0.01, 0.03, 0.5, 0.4)
# simple call with some explicit parameters, and slightly increased vol:
EuropeanOption(type="call", underlying=100, strike=100, dividendYield=0.01, 
riskFreeRate=0.03, maturity=0.5, volatility=0.5)
</pre>



<hr><div align="center">[Package <em>RQuantLib</em> version 0.1.14 <a href="00Index.html">Index]</a></div>

</body></html>
